My guess is he figured they would never play any of those songs without him, otherwise he would have negotiated it when they went through the legal stuff when he left the band. He probably thought, "I would never play this song or that song if the shoe were on the other foot," and figured they would extend the same courtesy regarding those seven songs, but he was wrong.
However, hasn't the charm of Dream Theater live always been, "Hey, they have a million songs and there is always a chance that any of them could be played on any given night." While the band doesn't rotate set lists the way they did for much of the 00s, they have done a tremendous job of playing different stuff from tour to tour with Mangini, and telling them, "You are not allowed to play Song a, b, c, d, e, f and g," would go against the very nature of who and what Dream Theater is. They probably still feel like they can play just about any song from any of their albums if they feel like it, and you cannot fault them for that. I do suspect that The Best of Times is the one song they will always feel is off the table.